# Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures

arXiv: https://arxiv.org/abs/2206.07588 · HTML: https://mlsanity.com/paper/2206.07588/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 49 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 10 of 10)

- [Learning Theory for Distribution Regression](https://mlsanity.com/paper/1411.2066/) (2014)
- [Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions](https://mlsanity.com/paper/1604.05251/) (2016)
- [Metrizing Weak Convergence with Maximum Mean Discrepancies](https://mlsanity.com/paper/2006.09268/) (2020)
- [A Kernel Two-Sample Test for Functional Data](https://mlsanity.com/paper/2008.11095/) (2020)
- [Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space](https://mlsanity.com/paper/1910.05954/) (2019)
- [Generalized Spectral Kernels](https://mlsanity.com/paper/1506.02236/) (2015)
- [Function-Space Distributions over Kernels](https://mlsanity.com/paper/1910.13565/) (2019)
- [Strictly proper kernel scores and characteristic kernels on compact spaces](https://mlsanity.com/paper/1712.05279/) (2017)
- [Kernels over Sets of Finite Sets using RKHS Embeddings, with Application to Bayesian (Combinatorial) Optimization](https://mlsanity.com/paper/1910.04086/) (2019)
- [Marginalising over Stationary Kernels with Bayesian Quadrature](https://mlsanity.com/paper/2106.07452/) (2021)

## Built on by (most cited first, 7 of 7)

- [Probabilistic neural operators for functional uncertainty quantification](https://mlsanity.com/paper/2502.12902/) (2025)
- [Data Reliability Scoring](https://mlsanity.com/paper/2510.17085/) (2025)
- [Uncertainty Quantification for Regression: A Unified Framework based on kernel scores](https://mlsanity.com/paper/2510.25599/) (2025)
- [Kernel Quantile Embeddings and Associated Probability Metrics](https://mlsanity.com/paper/2505.20433/) (2025)
- [Quantum-inspired probability metrics define a complete, universal space for statistical learning](https://mlsanity.com/paper/2508.21086/) (2025)
- [Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects](https://mlsanity.com/paper/2607.28981/) (2026)
- [Improving Function Space Flow Matching with Kernel Optimal Transport](https://mlsanity.com/paper/2609.38049/) (2026)

## Abstract (arXiv)

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes of kernels on Banach spaces and on metric spaces of strong negative type. The general results are used to give explicit classes of kernels on separable Lp spaces and on sets of measures.